Economic MPC with an Online Reference Trajectory for Battery Scheduling Considering Demand Charge Management

TL;DR

This paper tackles reducing monthly demand charges in microgrids with high renewable penetration by enhancing EMPC-based BESS dispatch with an online, short-horizon reference trajectory. It develops a two-stage framework: (i) online generation of a 24–48 h reference trajectory (with or without peak tracking) and (ii) an MPC stage that uses this trajectory in the terminal cost/constraints, including auxiliary states to track non-coincident and on-peak demand peaks. By comparing shrinking and rolling horizons across 24/48 h horizons with and without peak tracking on real data, the study shows that a 48 h rolling reference horizon yields the best economic performance, achieving cost reductions relative to a traditional EMPC benchmark. The approach is scalable, computationally tractable (convex optimization per step), and practical for real-time microgrid control, offering a path to lower monthly electricity costs in systems with demand charges.

Abstract

Monthly demand charges form a significant portion of the electric bill for microgrids with variable renewable energy generation. A battery energy storage system (BESS) is commonly used to manage these demand charges. Economic model predictive control (EMPC) with a reference trajectory can be used to dispatch the BESS to optimize the microgrid operating cost. Since demand charges are incurred monthly, EMPC requires a full-month reference trajectory for asymptotic stability guarantees that result in optimal operating costs. However, a full-month reference trajectory is unrealistic from a renewable generation forecast perspective. Therefore, to construct a practical EMPC with a reference trajectory, an EMPC formulation considering both non-coincident demand and on-peak demand charges is designed in this work for 24 to 48 h prediction horizons. The corresponding reference trajectory is computed at each EMPC step by solving an optimal control problem over 24 to 48 h reference (trajectory) horizon. Furthermore, BESS state of charge regulation constraints are incorporated to guarantee the BESS energy level in the long term. Multiple reference and prediction horizon lengths are compared for both shrinking and rolling horizons with real-world data. The proposed EMPC with 48 h rolling reference and prediction horizons outperforms the traditional EMPC benchmark with a 2% reduction in the annual cost, proving its economic benefits.

Figures (6)

• Figure 1: EMPC frameworks that include load and VRE forecasts, peak tracking, and reference trajectory methods for traditional (left) and proposed (right) EMPC. The following variables are presented: SOC of the BESS ($x$), charging/discharging power of the BESS ($u_2$), demand imported from the grid ($u_1$), forecasted load ($L_f$), forecasted PV generation ($PV_f$), NC and OP peak demands ($\hat{P}_{\text{NC}}$ and $\hat{P}_{\text{OP}}$), SOC of the BESS estimated as the reference trajectory ($x_r$), and demand imported from the grid estimated as the reference trajectory ($u_{r1}$).
• Figure 2: Temporal schematic example for a $48$ h prediction horizon together with a $48$ h reference horizon, both starting at time $t$, which falls on day $n$ of a month $M$ with $N$ days. The set of time points for the month $M$ is denoted by $\mathcal{T}_t$, with $\mathcal{T}_{\text{NC}, t}$ and $\mathcal{T}_{\text{OP}, t}$ defining the subsets corresponding to NC and OP demand charge periods, respectively. The final time points for these periods are represented as $\tau_{\text{NC},t}$ and $\tau_{\text{OP},t}$. The set $\mathcal{T}_{\text{OP}, t}$ is the union of the daily subset of OP demand charge time points $\mathcal{T}_{\text{OP}, t,n}$. Starting from $t$, the set of all time points in the reference horizon of length $T_{\text{R}}$ are defined in $\mathcal{T}_{\text{R},t}$, with its final time point called $\tau_{\text{R},t}$ and $\hat{\tau}_{\text{R},t}$ marking the time point at which the $50$% SOC low threshold is placed. Similarly, the prediction horizon starting at the time point $t$, with length $T_{\text{MPC}}$, is represented by $\mathcal{T}_{\text{MPC},t}$. The final time point in this horizon is $\tau_{\text{MPC},t}$, and $\hat{\tau}_{\text{MPC},t}$ identifies the time point at which the $50$% SOC low threshold is placed. Bold and unbold time parameters $\mathcal{T}_{\text{MPC},t}$, $\mathcal{T}_{\text{R},t}$,$T_{\text{MPC}}$, $T_{\text{R}}$, $\tau_{\text{MPC},t}$, $\tau_{\text{R},t}$, $\hat{\tau}_{\text{MPC},t}$, and $\hat{\tau}_{\text{R},t}$ designate rolling and shrinking horizons, respectively.
• Figure 3: Daily SOC difference between final and initial SOC (colored bars) together with daily NC peak (dashed gray line with "+" markers) and OP peak net loads (dotted gray line with "x" markers) in March 2019 for EMPC* and the following shrinking horizon cases: $\text{Trad}_{\rm WT}$ with $T_{\text{MPC}}=48$ h, and $\text{EMPC}_{\rm WT}$ with $T_{\text{R}}=T_{\text{MPC}}=48$ h. Cases with $T_{\text{MPC}}=24$ h have daily SOC difference equals zero because SOC starts and ends at $50$% every day.
• Figure 4: March 24 timeseries of $\text{Trad}_{\rm NT}$ with $T_{\text{MPC}}=24$ h, and $\text{EMPC}_{\rm NT}$ with $T_{\text{MPC}}=T_{\text{R}}=24$ h shrinking horizon cases for: (a) demand ($u_1$, solid lines) together with $\hat{y}_{\rm NC}(\tau_{\text{MPC},t}+1)$, $\check{y}_{\rm NC}(\tau_{\text{MPC},t}+1)$, and $\hat{P}_{\text{NC}}(t)$ for $\text{EMPC}_{\rm NT}$; and (b) SOC ($x$, dotted lines). The dotted gray line in (a) represents the net load, $L_{f}-\text{PV}_{f}$. The net load before 16:00 h is less than -100 kW due to solar over-generation.
• Figure 5: March 24 timeseries of (a) $u_1$, and (b) $x$, together with $\hat{y}_{\rm NC}(\tau_{\text{MPC},t}+1)$, $\check{y}_{\rm NC}(\tau_{\text{MPC},t}+1)$, $\hat{y}_{\rm OP}(\tau_{\text{MPC},t}+1)$, $\check{y}_{\rm OP}(\tau_{\text{MPC},t}+1)$, $\hat{P}_{\rm NC}(t)$, and $\hat{P}_{\rm OP}(t)$ for $\text{Trad}_{\rm WT}$ with $T_{\text{MPC}}=24$ h and $\text{EMPC}_{\rm WT}$ with $T_{\text{R}}=T_{\text{MPC}}=24$ h. All results are for rolling horizon cases.